Generalized fundamental equations on the submanifolds of a manifoldESX n

A connection which is both Einstein and semisymmetric is called anES connection, and a generalizedn-dimensional Riemannian manifold on which the differential geometric structure is imposed by a unified field tensorg through anES connection is called ann-dimensionalES manifold and denoted byESX _n . We investigate some necessary and sufficient conditions for submanifolds ofESX _n to be also Einstein and derive the generalized fundamental equations on various submanifolds ofESX _n , such as generalized Gauss formulas, generalized Weingarten equations, and generalized Gauss-Codazzi equations. We employ the useful and powerful concept ofC-nonholonomic frame of reference, introduced in earlier work.